Question

compute the derivative of the given function. f(x)=-4x^π + 6.1x^3.3+π^3.3 note: use pi for π in your answer. f(x)=□. hint: preview my answers submit answers your score was recorded. your score was successfully sent to the lms. you have attempted this problem 2 times. you received a score of 0% for this attempt. your overall recorded score is 0%. you have 4 attempts remaining.

Explanation:

Step1: Apply power - rule to first term

The power - rule for differentiation is $\frac{d}{dx}(ax^n)=nax^{n - 1}$. For the term $-4x^{\pi}$, we have $n = \pi$ and $a=-4$. So, $\frac{d}{dx}(-4x^{\pi})=-4\pi x^{\pi - 1}$.

Step2: Apply power - rule to second term

For the term $6.1x^{3.3}$, with $n = 3.3$ and $a = 6.1$, by the power - rule $\frac{d}{dx}(6.1x^{3.3})=6.1\times3.3x^{3.3 - 1}=20.13x^{2.3}$.

Step3: Differentiate the constant term

The derivative of a constant $C$ is 0. Since $\pi^{3.3}$ is a constant, $\frac{d}{dx}(\pi^{3.3}) = 0$.

Step4: Combine the derivatives

$f'(x)=\frac{d}{dx}(-4x^{\pi})+\frac{d}{dx}(6.1x^{3.3})+\frac{d}{dx}(\pi^{3.3})=-4\pi x^{\pi - 1}+20.13x^{2.3}+0$.

Answer:

$-4\pi x^{\pi - 1}+20.13x^{2.3}$